Assertion and Reason for Ch 1 Real Numbers Class 10 Math
Important QuestionsA
Directions : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Answer
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
1
Assertion (A): 13/3125 is a terminating decimal fraction.
Reason (R): If q = 2m 5n where m n, are non-negative integers, then p/q is a terminating decimal fraction.
Reason (R): If q = 2m 5n where m n, are non-negative integers, then p/q is a terminating decimal fraction.
Answer
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
We have 3125 = 55 = 55 × 20
Since the factors of the denominator 3125 is of the form 20 × 55, 13/3125 is a terminating decimal .
2
Assertion (A): 34.12345 is a terminating decimal fraction.
Reason (R): Denominator of 34.12345, when expressed in the form p/q, q ≠ 0, is of the form 2m × 5n , where m and n are non – negative integers.
Reason (R): Denominator of 34.12345, when expressed in the form p/q, q ≠ 0, is of the form 2m × 5n , where m and n are non – negative integers.
Answer
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
Its denominator is of the form 2m × 5n, where m = 5 and n = 4 which are non – negative integers.
3
Assertion (A): The HCF of two numbers is 5 and their product is 150, then their LCM is 30.
Reason (R): For any two positive integers a and b, HCF(a, b) + LCM(a , b) = a × b .
Reason (R): For any two positive integers a and b, HCF(a, b) + LCM(a , b) = a × b .
Answer
(c) Assertion (A) is true but reason (R) is false.
We have,
LCM(a, b) × HCF(a, b) = a × b
LCM × 5 = 150
LCM = 150/5 = 30